Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch

Monday, December 08, 2008

A job posting for THEORY-Univ of Michigan

(Guest Post from Anna Gilbert from Univ of Michigan.
Its actually a pointer to a job posting in theory!)

We have an opening for a postdoctoral fellow in Theoretical Computer
Science at the University of Michigan. This is a joint position
between the Department of Mathematics and the Department of Computer
Science Engineering. Please apply by January 1, 2009 when we start
reviewing applications.

In the recently published "Princeton Companion to Mathematics" (*extremely* highly recommended btw; even if you are starving postdoc at UoM buy this), the introductory section on theoretical computer science (pp. 7) has this tosay -- "... Thus, theoretical computer science is a genuine branch of pure mathematics: in theory, one could be an excellent computer scientist and be unable to program a computer. However, it has had many notable applications as well ..."

Why should "pure mathematicians" who are theoretical computer scientists get more privileges than the others ? In any case 1+1 teaching load is better than 2+2 or 2+1 that most math postdocs get. UoM Math Dept. is as good as it gets -- just get them to promise ahead of time that they will not make you teach the Math 115/116 sequence.

The certainty about the limited length of the term of appointment, together with the mandatory teaching makes it hard. In a typical postdoc (such as the NSF Math Sciences postdocs) the teaching is optional or not every term. It is useful to get teaching experience but it can be important for a postdoc to be able to travel during the academic term for research exposure or for interviews and both of these are made harder by teaching commitments.

Correct me if I am wrong; but I think most of the super-prestigious post-doctoral positions such as Dickson/Benjamin Pierce/Gibbs/Courant Instructorships/ Hildebrandt's etc. all come with some teaching (might be 1+1) or at least did in my times. So 1+1 is not a bad load at all. One can easily find sympathetic colleagues to substitute if one has to travel during the semester. Moreover, the teaching experience is vital when applying for tt positions in mathematics since most departments need a teaching letter.

On a larger scale,I think given the disconnect between theoretical CS and the rest of the engineering-minded sub-disciplines of CS, many (if not most) theoreticians will seek refuge in math departments -- so we should all get used to the culture of mathematics.

I'm a first-year grad student CS trying to decide whether to go into theory. I definitely find it the most interesting of areas, but I'm concerned about finding a job after I graduate. Is the situation really that dire? Is it just that jobs at top universities are hard to find, or is this true across the board?

...given the disconnect between theoretical CS and the rest of the engineering-minded sub-disciplines of CS,

You say this as we didn't have a say on this. Situation is to the contrary. Areas of TCS that stay relevant will see increased funding, while areas that seek complexity for complexity's sake will wither and die.

A good example of this is bioinformatics, which many distinguished theoretical computer scientists have found to be a rich source of problems and funding. Ditto for data streams, network algorithms, ad auctions, game theory, among others.

I can see modern complexity theorists working in math departments. But many other areas of theory wouldn't fit, because they don't contain very much mathematical depth. This isn't a knock on them -- they've shown that its possible to study very interesting models with elementary techniques. Nevertheless, its certainly not mathematics.

I'm a first-year grad student CS trying to decide whether to go into theory... Is the situation really that dire?

It is hard to predict the job situation 5 years out, which is what matters to you. Things are cyclical. The early to mid 90's were very tough for theory graduates with greatly increased numbers of CS PhD grads, flat undergrad enrollments and the old line industrial research labs contracting, sending strong senior people out to universities where they had the best shot at jobs. On top of that, NSF funding was flat, too. Just a couple of years later things had turned around completely and large numbers of places for theoreticians opened up both in academia with booming enrollments and in the new industrial research labs. Howver, right now, graduating as a new PhD in any field of CS looks pretty tough if you want an academic job.

On the other hand, government support for the sciences and undergrad CS enrollments are picking up, and it isn't as though the influence of IT has declined. Unlike the mid 90's there seems to be a general realization, based on the success of companies like Google, that you're not going to make progress without paying attention to a theoretical viewpoint as well as one based on hacking up something that seems OK. Smarts matter.

I'm a first-year grad student CS trying to decide whether to go into theory. I definitely find it the most interesting of areas, but I'm concerned about finding a job after I graduate.

This should not be a consideration.

In his essay on "Advice to young mathematicians" Bella Bolobas says --" ... Do mathematics only if you are passionate about it, only if you would do even if you had to find the time for it after a full day's work in another job. Like poetry and music, mathematics is not an occcupation but a vocation."(The Princeton Companion to Mathematics, pp. 1004).Same applies to theoretical computer scientists as they are pure mathematicians after all (loc.cit. pp. 7),

As a practical matter, given the time pressures on a professor at a typical US university (teaching, committee work, sifting through applications etc.) it might be more effective to do mathematics on the side, and have a mindless day job (say in the banking or the financial industry). That way you can live in a big city, earn more for your family, and at the same time have more time to think and write papers.

Anonymous says: "[given the dismal job market] it might be more effective to do mathematics on the side."

The type specimen of this career strategy is the composer Charles Ives (insurance executive) of whom Shoenberg famously said "There is a great man living in this country – a composer. He has solved the problem how to preserve one's self and to learn. He responds to negligence by contempt. He is not forced to accept praise or blame. His name is Ives."

In the mathematical field, there is Poincare (mining engineer), von Neumann (in his later years a system engineer), and David E. Shaw (financial engineer) ... and probably many more.

----

Also, with regard to the one-per-million incidence of AMS-advertised academic jobs, there is striking geographic variability in this incidence.

Here in Washington state, there is *one* (!) advertised mathematics job for a state population of six million.

Brrrrrr ... and several states have zero AMS-advertised jobs: Hawaii, Idaho, Kansas, Montana, Nevada, North Dakota, Vermont, West Virginia, and Wyoming.

Areas of TCS that stay relevant will see increased funding, while areas that seek complexity for complexity's sake will wither and die.

This position sounds dangerous, and, as far as I'm concerned, the STOC96 Goldreich-Wigderson position paper addressed it well. To cite one example from there, Valiant introduced concentrators to solve a problem with "no" practical applications... and concentrators and expanders have since become influential.

I have no problem with the idea that certain "hot" topics might receive extra funding. However, to starve "pure complexity" until it dies off is missing the point. I can even use myself as an example: I recently published a paper on biomolecular computing, and Bill has put it on his "Applications of Ramsey Theory" web site. New hot topic, meet pure complexity.

For whatever it's worth, my strategic assessment of the field is that there is an unhealthy disconnect between the hot-topic-ers and the "purists." I believe there is a tremendous toolbox already available from research in pure complexity, and it is barely being applied to emerging models of computation. I've begun to write things that attempt to build a bridge between the two areas, and I think a lot more of that needs to be done.

Proving non-linear bounds for any problem in P, given that we have so few, is clearly a fundamental contribution likely to advance the state of theory and practice.

Perhaps my ealier post was unintentionally misleading, given the examples used. It is possible for TCS to stay relevant and applied even while it pursues questions with no immediate practical applications. What I'm arguing for is that we should remain sensitive to whether we are pursuing deep avenues of research, likely to be of used at some point in the future, or if we are pursuing complexity for complexity's sake, beating dead horses and following dead ends.

To give an example, I once saw a journal paper which studied the intricacies of search data structures that hold very few elements. Now in practice if one had so few elements a simple linear search would suffice. Hence naively one could claim these results had no applications. Yet, a quick leafing through the paper suggested that to the contrary, it was extremely applied in that the line of attack was such that lessons learned in this simple case seemed highly like to be useful for optimizing general search data structures such as Van Emde Boas trees.

That is the power of theory. It is unencumbered by immediate applications, but it should not be blind to eventual applicability.

What I'm arguing for is that we should remain sensitive to whether we are pursuing deep avenues of research, likely to be of used at some point in the future, or if we are pursuing complexity for complexity's sake, beating dead horses and following dead ends.

As they say -- hindsight is 20/20, but it is not easy to determine which problems are important and which are not. In fact the driving problems in many areas of pure mathematics are not all that important (think Goldbach or twin primes conjectures or even Fermat's theorem), but they drive research by the reasoning -- if we cannot resolve these problems then something must be missing in our understanding (of primes in this case). The same is probably true of the various itty-bitty results in computational complexity theory and more generally in extremal combinatorics. In short, the lesson here is, if its simple to state and difficult to resolve, then there is probably something interesting lurking underneath.

As they say -- hindsight is 20/20, but it is not easy to determine which problems are important and which are not.

It is not easy, but what are you suggesting then, that we do not try at all? That would be even worse.

many areas of pure mathematics are not all that important (think Goldbach or twin primes conjectures or even Fermat's theorem), but they drive research by the reasoning

Funny that you mention Fermat. Andrew Wiles being an outstanding mathematician didn't work on the FLT until he could do quality mathematics in the process of resolving the question.

In short, the lesson here is, if its simple to state and difficult to resolve, then there is probably something interesting lurking underneath.

What you are suggesting here is nothing but one way to predict long term applicability. This one, together with others can be used to judge the current level of promise of an area and consequently the best allocation of resources at the present time.

Is it just that jobs at top universities are hard to find, or is this true across the board?

My take:- Academic jobs in any area are extremely hard to get right now. Historically speaking, though, and all other things being equal, it is probably easier to get an academic job in any area other than TCS.

- Having said that, there are certain areas of TCS that are "hot" right now and may remain so in 5 years. These include bioinformatics and game theory.

- Graduate students in TCS do just fine on the general (non-research track) job market. It is even possible they may have a slight edge. This assumes you have basic programming skills.

The upshot: if you enjoy TCS, are good at it, and do not necessarily have your heart set on an academic job, go for it. If your goal is an academic job, try to make your work practically relevant or work in one of the "hot" areas of TCS like those mentioned above.

I think the Bollobas quote is garbage. I think most people MUST think ahead to the future.

I think the Bollobas quote is garbage. I think most people MUST think ahead to the future.

Don't be too quick to dismiss what Bollobas is saying. The quote is not intended for people whose ultimate objective is to find "a tt position" in an R1. Such people can pursue the hot or the cold or do any number of things suggested in this forum and attain their objective and live happily thereafter enjoying the cozy life in the generic moo-ville.

However, if one wants to pursue mathematics then these matters are irrelevant. The greatest mathematicians of the last century had wanderedthe globe with temporary positions before they got famous. Grothendieck is an extreme example -- I hear they preserved the blackboard he used in U of K...

Anonymous says: "The greatest mathematicians of the last century had wandered the globe with temporary positions before they got famous. Grothendieck is an extreme example -- I hear they preserved the blackboard he used in U of Kansas."

Just as a point of interest, Kansas is one of the ten states having *zero* AMS jobs listed this year ... which is sad news for all the young Grothendiecks out there.

Only now are we engineers getting around to making practical use of some of Grothendieck's tensor product investigations of the early 1950s ... the point being, that in practice the "sowing and reaping" of fundamental mathematical ideas takes decades.

Opportunities for young people lost now cannot easily be remediated later.

The greatest mathematicians of the last century had wanderedthe globe with temporary positions before they got famous.

The point is that most people can't live like this -- they want to get married, have kids, settle down, have a life outside of math, etc. Most people would not be interested in being Erdos, even if given the chance.

It's just another idea that sounds great in theory but doesn't work (for most people) in practice.

It's just another idea that sounds great in theory but doesn't work (for most people) in practice.

It's worse than that: in practice the idea is just an excuse for people to brag about their dedication without ever having to make good on their boasts.

For example, Bollobas has never faced a career difficulty greater than deciding whether to leave Cambridge to be a big fish in a small pond. It's easy for him to say every mathematician should be prepared to do research in the evenings after a full-time job.

Anonymous posts: "[It's too easy] to say every mathematician should be prepared to do research in the evenings after a full-time job."

Anonymous IMHO has the right of it. But rather than make the case ab initio, I will note that Bjarne Stroustrup has a lengthy interview in this month's Datamation (accessible via SlashDot) that touches on many CS and TCS-related issues that have been mentioned in this thread.

It is only necessary to mentally substitute the word "theorem" for "code" in reading Stroustroup's essay.

E.g., this quote: "It is rare that anyone thinks about the structure of their code or the implications for scaling and maintenance – those are not academic subjects. Students are taught good practical and essential topics, such as algorithms, data structures, machine architecture, programming languages, and 'systems,' but only rarely do they 'connect the dots' to see how it all fits together in a maintainable program."

Also: "Serious programming is a team sport, so brush up on your social skills."

Just as Stroustrup is right that CS has to be concerned with more than writing code, doesn't TCS have to be concerned with more than proving theorems?

To me, it seems like common sense that all of us living on our overheated planet---whose ecosystems are steadily degrading, and that presently has six-going-on-ten billion people on living on it (that's a lot of humanity)---simply cannot afford to embrace narrowly defined or isolationist conceptions of science, engineering, or mathematics.

As in the memorable scene in Apollo 13, it's instead time to ask, in the broadest possible sense: "What have we got on the spaceship that's good?"

To my mind, it is insufficiently appreciated by engineers---and arguably insufficiently appreciated by mathematicians themselves---that modern mathematics (and information theory especially) is among the most valuable and potent resources that our spaceship has on-board.

The point is that most people can't live like this -- they want to get married, have kids, settle down, have a life outside of math, etc. Most people would not be interested in being Erdos, even if given the chance.

Very true -- but then they should not expect cushy jobs in mathematics and not complain if they do not get them.One cannot have it both ways. After all there are lucrative careers to be made in many other areas not demanding of such big sacrifices in life.

Anonymous, you state this as an axiom, but it should be noted that it is a very dubious axiom, and many mathematicians and scientists have disagreed with it.

Dirac (for example): "[In the early days of quantum mechanics] It was a good description to say that it was a game, a very interesting game one could play. Whenever one solved one of the little problems, one could write a paper about it. It was very easy in those days for any second-rate physicist to do first-rate work."

From Dirac's point of view, modern mathematics in general (and TCS in particular) is *not* (or should not be) all about achieving the very highest ranks within academic disciplines that are very difficult and within which jobs are very scarce.

Because the consequent emphasis on academic ranking would lead students to embrace---with relative passivity---a world-view that (from a global point of view) would be pointlessly dystopian, needlessly inhumane, and worst of all, too isolated to help our planet grapple effectively with the very real and very urgent challenges we face.

Well, before this thread drops off Lance's front page, this would be a good time to say that the arxiv preprint Combining geometry and combinatorics: A unified approach to sparse signal recovery, by Anna Gilbert and her colleagues---also the accompanying talks that can be found on-line---was (IMHO) a really nice example of mathematical work bridging from the fundamental to the applied; the kind of work that in the long run benefits everyone.

Commentary on the job market aside, I thought I'd clear up a few factual details.

Yes, the position is for 3 years. You can shorten that if you like but we guarantee a job for three years.

The teaching load is 1+1, one course in Mathematics and one in Computer Science. (The typical math postdoc load is 2+2 and that for CS is 0+0. You do the math...)

There are faculty in both the Mathematics and Computer Science Departments who have interests in theoretical computer science so Theory is split across the two departments, hence an usual position. This should not be taken as any real commentary on the importance of theory to either department. UMichigan's a big school and there are faculty affiliated with the theory group in several departments across campus.

It's a fun place and we look forward to welcoming a new colleague next fall!